| 1. |
- Chhabra, Robin, et al.
(författare)
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A generalized exponential formula for forward and differential kinematics of open-chain multi-body systems
- 2014
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Ingår i: Mechanism and machine theory. - : Elsevier BV. - 0094-114X .- 1873-3999. ; 73, s. 61-75
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a generalized exponential formula for Forward and Differential Kinematics of open-chain multi-body systems with multi-degree-of-freedom, holonomic and nonholonomic joints. The notion of lower kinematic pair is revisited, and it is shown that the relative configuration manifolds of such joints are indeed Lie groups. Displacement subgroups, which correspond to different types of joints, are categorized accordingly, and it is proven that except for one class of displacement subgroups the exponential map is surjective. Screw joint parameters are defined to parameterize the relative configuration manifolds of displacement subgroups using the exponential map of Lie groups. For nonholonomic constraints the admissible screw joint speeds are introduced, and the Jacobian of the open-chain multi-body system is modified accordingly. Computational aspects of the developed formulation for Forward and Differential Kinematics of open-chain multi-body systems are explored by assigning coordinate frames to the initial configuration of the multi-body system, employing the matrix representation of SE(3) and choosing a basis for se(3). Finally, an example of a mobile manipulator mounted on a spacecraft, i.e., a six-degree-of-freedom moving base, elaborates the computational aspects. © 2013 Elsevier Ltd.
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| 2. |
- Chhabra, Robin, et al.
(författare)
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A holistic approach to concurrent engineering and its application to robotics
- 2014
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Ingår i: Concurrent Engineering - Research and Applications. - 1063-293X .- 1531-2003. ; 22:1, s. 48-61
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Tidskriftsartikel (refereegranskat)abstract
- This article details a holistic concurrent design framework, based on fuzzy logic, which is suitable for multidisciplinary systems. The methodology attempts to enhance communication and collaboration between different disciplines through introducing the universal notion of satisfaction and expressing the holistic behavior of multidisciplinary systems using the notion of energy. Throughout the design process, it uses fuzzy logic to formalize subjective aspects of design including the impact of the designer's attitude, resulting in the simplification of the multi-objective constrained optimization process. In the final phase, the methodology adjusts the designer's subjective attitude based on a holistic system performance by utilizing an energy-based model of multidisciplinary systems. The efficiency of the resulting design framework is illustrated by improving the design of a 5-degree-of-freedom industrial robot manipulator. © The Author(s) 2013.
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| 3. |
- Chhabra, Robin, et al.
(författare)
-
A holistic concurrent design approach to robotics using hardware-in-the-loop simulation
- 2013
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Ingår i: Mechatronics (Oxford). - : Elsevier BV. - 0957-4158 .- 1873-4006. ; 23:3, s. 335-345
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Tidskriftsartikel (refereegranskat)abstract
- This paper discusses a practical approach to the concurrent design of robot manipulators, which is based on an alternative design methodology, namely Holistic Concurrent Design (HCD), as well as the utilization of a modular hardware-in-the-loop simulation. Holistic concurrent design is a systematic design methodology for mechatronic systems that formalizes subjective notions of design, resulting in the simplification of the multi-objective constrained optimization process. Its premise is to enhance the communication between designers with various backgrounds and customers, and to consider numerous design variables with different natures concurrently. The methodology redefines the ultimate goal of design based on the qualitative notion of satisfaction, and formalizes the effect of designer's subjective attitude in the process. The hardware-in-the-loop platform involves physical joint modules and the control unit of a manipulator in addition to the software simulation to reduce modeling complexities and to take into account physical phenomena that are hard to be captured mathematically. This platform is implemented in the HCD design architecture to reliably evaluate the design attributes and performance supercriterion during the design process. The resulting architecture is applied to redesigning kinematic, dynamic and control parameters of an industrial manipulator. Copyright © 2013 Published by Elsevier Ltd. All rights reserved.
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| 4. |
- Chhabra, Robin, et al.
(författare)
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A linguistic approach to concurrent design
- 2015
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Ingår i: Journal of Intelligent & Fuzzy Systems. - 1064-1246 .- 1875-8967. ; 28:5, s. 1985-2001
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Tidskriftsartikel (refereegranskat)abstract
- This paper outlines a concurrent design methodology for multidisciplinary systems, which employs tools of fuzzy theory for the tradeoff in the design space. This methodology enhances communication between designers from various disciplines through introducing the universal notion of satisfaction and expressing the behaviour of multidisciplinary systems using the notion of energy. It employs fuzzy rule-bases, membership functions and parametric connectives in fuzzy logic to formalize subjective aspects of design, resulting in a two-phase simplification of the multi-objective constrained optimization of a design process. The methodology attempts to find a pareto-optimal solution for the design problem. In the primary phase of the methodology, a fuzzy-logic model is utilized to identify a region in the design space that contains the pareto-optimal design state, and a proper initial state is suggested for the optimization in the secondary phase, where the pareto-optimal solution is found. Finally, the impact of the designer's subjective attitude on the design is adjusted based on a system performance by utilizing an energy-based model of multidisciplinary systems. As an application, it is shown that the design of a five-degree-of-freedom industrial robot manipulator can be enhanced by using the methodology.
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| 5. |
- Chhabra, Robin, et al.
(författare)
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A Unified Approach to Input-output Linearization and Concurrent Control of Underactuated Open-chain Multi-body Systems with Holonomic and Nonholonomic Constraints
- 2016
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Ingår i: Journal of dynamical and control systems. - : Springer Science and Business Media LLC. - 1079-2724 .- 1573-8698. ; 22:1, s. 129-168
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a unified geometric framework to input-output linearization of open-chain multi-body systems with symmetry in their reduced phase space. This leads us to an output tracking controller for a class of underactuated open-chain multi-body systems with holonomic and nonholonomic constraints. We consider the systems with multi-degree-of-freedom joints and possibly with non-zero constant total momentum (in the holonomic case). The examples of these systems are free-base space manipulators and mobile manipulators. We first formalize the control problem, and rigorously state an output tracking problem for such systems. Then, we introduce a geometrical definition of the end-effector pose and velocity error. The main contribution of this paper is reported in Section 5, where we solve for the input-output linearization of the highly nonlinear problem of coupled manipulator and base dynamics subject to holonomic and nonholonomic constraints. This enables us to design a coordinate-independent controller, similar to a proportional-derivative with feed-forward, for concurrently controlling a free-base, multi-body system. Finally, by defining a Lyapunov function, we prove in Theorem 3 that the closed-loop system is exponentially stable. A detailed case study concludes this paper.
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| 6. |
- Chhabra, Robin, et al.
(författare)
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Concurrent synthesis of robot manipulators using hardware-in-the-loop simulation
- 2009
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Ingår i: IEEE International Conference on Robotics and Automation, ICRA, Kobe, Japan, 12-17 May 2009. - Piscataway, NJ : IEEE Communications Society. - 9781424427895 ; , s. 568-573
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Konferensbidrag (refereegranskat)abstract
- This paper discusses a practical approach to the concurrent synthesis of robot manipulators, which is based on the alternative design methodology of Linguistic Mechatronics (LM) as well as the utilization of a modular Robotic Hardwarein- the-loop Simulation (RHILS) platform. The RHILS platform involves physical joint modules and the control unit to reduce modeling complexities while taking into account various physical phenomena. The LM methodology simplifies the multi-objective constrained optimization problem into a singleobjective unconstrained formulation and also brings subjective notions of design into the scope. The new approach is applied to redesigning kinematic, dynamic and control parameters of an industrial manipulator. © 2009 IEEE.
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| 7. |
- Chhabra, Robin, et al.
(författare)
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Holistic system modeling in mechatronics
- 2011
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Ingår i: Mechatronics (Oxford). - : Elsevier BV. - 0957-4158 .- 1873-4006. ; 21:1, s. 166-175
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Tidskriftsartikel (refereegranskat)abstract
- This paper outlines an alternative modeling scheme for mechatronic systems, as a basis for their concurrent design. The approach divides a mechatronic system into three generic subsystems, namely generalized executive, sensory and control, and links them together utilizing a combination of bond graphs and block diagrams. It considers the underlying principles of a multidisciplinary system, and studies the flow of energy and information throughout its different constituents. The first and second laws of thermodynamics are reformulated for mechatronic systems, and as a result three holistic design criteria, namely energy, entropy and agility, are defined. These criteria are formulated using the bond graph representation of a mechatronic system. As a case study, the three criteria are employed separately for concurrent design of a five degree-of-freedom industrial robot manipulator. © 2010 Elsevier Ltd. All rights reserved.
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| 8. |
- Chhabra, Robin, et al.
(författare)
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Linguistic mechatronics
- 2008
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Ingår i: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM, Xi'an, China, 2-5 July 2008. - Piscataway, NJ : IEEE Communications Society. - 9781424424955 ; , s. 1315-1320
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Konferensbidrag (refereegranskat)abstract
- This paper outlines a systematic design methodology for mechatronic systems, which formalizes subjective notions and simplifies the optimization process, in the hope that communication between designers with various backgrounds and clients is enhanced and numerous design variables with different natures can be considered concurrently. The methodology redefines the ultimate goal of design based on the qualitative notions of wish and must satisfaction, and formalizes the effect of designer's subjective attitude in the process, which can be adjusted based on the reality of system performance. © 2008 IEEE.
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| 9. |
- Chhabra, Robin, et al.
(författare)
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Nonholonomic dynamical reduction of open-chain multi-body systems : A geometric approach
- 2014
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Ingår i: Mechanism and machine theory. - : Elsevier BV. - 0094-114X .- 1873-3999. ; 82, s. 231-255
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Tidskriftsartikel (refereegranskat)abstract
- This paper studies the geometry behind nonholonomic Hamilton's equation to present a two-stage reduction procedure for the dynamical equations of nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. In this process, we use the Chaplygin reduction and an almost symplectic reduction theorem. We first restate the Chaplygin reduction theorem on cotangent bundle for nonholonomic Hamiltonian mechanical systems with symmetry. Then, under some conditions we extend this theorem to include a second reduction stage using an extended version of the symplectic reduction theorem for almost symplectic manifolds. We briefly introduce the displacement subgroups and accordingly open-chain multi-body systems consisting of such joints. For a holonomic open-chain multi-body system, the relative configuration manifold corresponding to the first joint is a symmetry group. Hence, we focus on a class of nonholonomic distributions on the configuration manifold of an open-chain multi-body system that is invariant under the action of this group. As the first stage of reduction procedure, we perform the Chaplygin reduction for such systems. We then introduce a number of sufficient conditions for a reduced system to admit more symmetry due to the action of the relative configuration manifolds of other joints. Under these conditions, we present the second stage of the reduction process for nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. Finally, we explicitly derive the reduced dynamical equations in the local coordinates for an example of a two degree-of-freedom crane mounted on a four-wheel car to illustrate the results of this paper.
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| 10. |
- Chhabra, Robin, et al.
(författare)
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Reduction of Hamiltonian Mechanical Systems With Affine Constraints : A Geometric Unification
- 2017
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Ingår i: Journal of Computational and Nonlinear Dynamics. - : The American Society of Mechanical Engineers (ASME). - 1555-1415 .- 1555-1423. ; 12:2
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a geometrical approach to the dynamical reduction of a class of constrained mechanical systems. The mechanical systems considered are with affine nonholonomic constraints plus a symmetry group. The dynamical equations are formulated in a Hamiltonian formalism using the Hamilton-d'Alembert equation, and constraint forces determine an affine distribution on the configuration manifold. The proposed reduction approach consists of three main steps: (1) restricting to the constrained submanifold of the phase space, (2) quotienting the constrained submanifold, and (3) identifying the quotient manifold with a cotangent bundle. Finally, as a case study, the dynamical reduction of a two-wheeled rover on a rotating disk is detailed. The symmetry group for this example is the relative configuration manifold of the rover with respect to the inertial space. The proposed approach in this paper unifies the existing reduction procedures for symmetric Hamiltonian systems with conserved momentum, and for Chaplygin systems, which are normally treated separately in the literature. Another characteristic of this approach is that although it tracks the structure of the equations in each reduction step, it does not insist on preserving the properties of the system. For example, the resulting dynamical equations may no longer correspond to a Hamiltonian system. As a result, the invariance condition of the Hamiltonian under a group action that lies at the heart of almost every reduction procedure is relaxed
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